This thesis presents some results in the theory of optimal linear regression design with a general concave criterion function &phis;. A summary is given of relevant known work in the theory of optimal linear regression design for several criteria of optimality and it is shown how this can be extended to fit into a general framework. In particular an equivalence theorem for the general concave criterion function &phis; is presented with emphasis on the role of differentiability of &phis;. Algorithms are discussed in this general context and their convergence is established under certain conditions on &phis;. In the final chapter the asymptotic rate of convergence of these algorithms is discussed.